Most blown-up option accounts were not wrecked by picking the wrong trade. They were wrecked by a reasonable trade at the wrong size. Position sizing answers the question the rest of the course leaves open: now that you know what to trade, how many contracts?
Start from a risk budget
A risk budget is the most you will lose on one trade, set as a fixed share of the account before you look at the trade. Many traders use 1% to 2%; on a $50,000 account at 2%, that is $1,000 a trade. Setting it in advance stops the size from growing with your enthusiasm, and as a percentage it shrinks after losses and grows after gains on its own. There are three ways to turn it into contracts, one for each kind of risk.
Sizing by maximum loss
When the worst case is fixed, divide. A long call bought for $3.20 can lose $320 a contract, so the $1,000 budget buys three ($960), not four. A put credit spread with a $380 maximum loss allows two. This is the cleanest method, and the reason defined-risk structures are easy to size. Round down, never up, and count the whole premium as at risk: a long option can, and often does, go to zero.
Sizing by the one-sigma move
A short option or a stock position has no maximum loss to divide by, so size it by the move the market is pricing. From Module 4, one standard deviation to expiration is the stock price times the implied volatility times the square root of the time: S × IV × √(days / 365). A $200 stock at 25% volatility, 30 days out, has a one-sigma move of about $14.33.
A $100 stock at 25% volatility, 30 days out. The darker band is one standard deviation, the lighter one two. Drag days or volatility and watch the range your position has to survive widen.
About two times in three the stock ends inside the darker band; about one time in twenty it ends outside the lighter one. Work out what your position loses on a one-sigma move against you and keep that inside the budget, then check the two-sigma loss and make sure you could live with it. The at-the-money straddle is worth about 0.8 of one sigma, so it doubles as a check on your arithmetic.
Sizing by vega
When the trade is a view on volatility, the risk is volatility moving the wrong way, so size by vega: dollars gained or lost for each one-point change in implied volatility. Say a 60-day at-the-money straddle has a vega of 0.32 per share, $32 a contract, so ten straddles carry $320 a vol point. If implied volatility could plausibly drop 6 points, after an event or in a calm week, that is $1,920 at risk, nearly twice a $1,000 budget. Five straddles fit.
Vega per share of a $100 call against days to expiration, at the money and 10% out. Hover at 10 days and at 90: the longer option carries about three times the volatility risk per contract. Raise volatility and the out-of-the-money line climbs toward the at-the-money one.
Vega grows with time to expiration: ten 90-day options carry about three times the vega of ten 10-day options at the same strike. Size each trade by its vega in dollars, not by its contract count.
Correlated positions are one bet
Short puts on five chip stocks are not five trades. They are one bet on the chip sector, and in a selloff the stocks fall together: correlation, how closely two prices move together, climbs toward one exactly when you need it low. Add up the risk of positions that move together and size the group as one position. The same goes for a call on a stock and a call on an ETF that holds it.
Sizing short premium for the tail day
Selling premium wins small amounts often and loses large amounts rarely, so size it for the rare day, the one in the tail of the distribution. Sell a $90 put and a $110 call on a $100 stock for about $1.06, 30 days out at 30% volatility. On an ordinary day the position earns a few dollars of time decay per contract. If the stock gaps to $80 the next morning and volatility jumps to 50%, the strangle loses about $1,010 a contract, close to ten times what it collected.
Short the $90 put and the $110 call, 30 days out at 30% volatility. The flat top is the credit; past the strikes the loss grows a dollar for every dollar the stock moves. Set volatility to 50% with 29 days left and hover at $80 to see the morning after a gap.
If the worst day you are prepared to take is $2,000, two of these strangles fit, even though the margin from the last lesson might let you sell ten. The margin requirement tells you what the broker will allow; the tail day tells you what you can survive.
The maths: three sizing rules, and how correlated risks add
With a risk budget B:
- By maximum loss
Lper contract:contracts = floor(B / L). - By the one-sigma move
σ$ = S × IV × √(t / 365), for a position that loses aboutDdollars per contract for each dollar the stock moves against it:contracts = floor(B / (D × σ$)). This straight-line estimate understates the loss on a short option, because gamma makes the loss grow faster than the move. - By vega, with vega
Vper share and a plausible volatility change ofΔvpoints:contracts = floor(B / (100 × V × Δv)).
Worked example for the vega rule: B = 1,000, V = 0.32, Δv = 6, so 1,000 / (100 × 0.32 × 6) = 1,000 / 192 = 5.2, which rounds down to five straddles.
For several positions, one-sigma risks combine as σ_total² = Σ σ_i² + 2 Σ ρ_ij σ_i σ_j, where ρ_ij is the correlation between each pair. Three positions that each risk $1,000 at one sigma risk √3 × 1,000 ≈ $1,732 together if they are unrelated (ρ = 0), and the full $3,000 if they move as one (ρ = 1). A selloff pushes ρ toward 1, which is why the group should be sized as one bet.
Your turn
Open NVDA on the Options Chain at the monthly expiration and read what one at-the-money call can lose. Then switch to IWM, work out its one-sigma move to the monthly expiration, and read the vega of its at-the-money call.